Politicians who talk about the terrorism threat -- and it's already clear that this will be a polarizing issue in the 2008 campaign -- should be required to read a new book by a former CIA officer named Marc Sageman. It stands what you think you know about terrorism on its head and helps you see the topic in a different light.

Sageman has a résumé that would suit a postmodern John le Carré. He was a case officer running spies in Pakistan and then became a forensic psychiatrist. What distinguishes his new book, "Leaderless Jihad," is that it peels away the emotional, reflexive responses to terrorism that have grown up since Sept. 11, 2001, and looks instead at scientific data Sageman has collected on more than 500 Islamic terrorists -- to understand who they are, why they attack and how to stop them.

The heart of Sageman's message is that we have been scaring ourselves into exaggerating the terrorism threat -- and then by our unwise actions in Iraq making the problem worse. He attacks head-on the central thesis of the Bush administration, echoed increasingly by Republican presidential candidate John McCain, that, as McCain's Web site puts it, the United States is facing "a dangerous, relentless enemy in the War against Islamic Extremists" spawned by al-Qaeda.

The numbers say otherwise, Sageman insists. The first wave of al-Qaeda leaders, who joined Osama bin Laden in the 1980s, is down to a few dozen people on the run in the tribal areas of northwest Pakistan. The second wave of terrorists, who trained in al-Qaeda's camps in Afghanistan during the 1990s, has also been devastated, with about 100 hiding out on the Pakistani frontier. These people are genuinely dangerous, says Sageman, and they must be captured or killed. But they do not pose an existential threat to America, much less a "clash of civilizations."

It's the third wave of terrorism that is growing, but what is it? By Sageman's account, it's a leaderless hodgepodge of thousands of what he calls "terrorist wannabes." Unlike the first two waves, whose members were well educated and intensely religious, the new jihadists are a weird species of the Internet culture. Outraged by video images of Americans killing Muslims in Iraq, they gather in password-protected chat rooms and dare each other to take action. Like young people across time and religious boundaries, they are bored and looking for thrills.

"It's more about hero worship than about religion," Sageman said in a presentation of his research last week at the New America Foundation, a liberal think tank here. Many of this third wave don't speak Arabic or read the Koran. Very few (13 percent of Sageman's sample) have attended radical madrassas. Nearly all join the movement because they know or are related to someone who's already in it. Those detained on terrorism charges are getting younger: In Sageman's 2003 sample, the average age was 26; among those arrested after 2006, it was down to about 20. They are disaffected, homicidal kids -- closer to urban gang members than to motivated Muslim fanatics.

Sageman's harshest judgment is that the United States is making the terrorism problem worse by its actions in Iraq. "Since 2003, the war in Iraq has without question fueled the process of radicalization worldwide, including the U.S. The data are crystal clear," he writes. We have taken a fire that would otherwise burn itself out and poured gasoline on it.

The third wave of terrorism is inherently self-limiting, Sageman continues. As soon as the amorphous groups gather and train, they make themselves vulnerable to arrest. "As the threat from al-Qaeda is self-limiting, so is its appeal, and global Islamist terrorism will probably disappear for internal reasons -- if the United States has the sense to allow it to continue on its course and fade away."

Sageman's policy advice is to "take the glory and thrill out of terrorism." Jettison the rhetoric about Muslim extremism -- these leaderless jihadists are barely Muslims. Stop holding news conferences to announce the latest triumphs in the "global war on terror," which only glamorize the struggle. And reduce the U.S. military footprint in Iraq, which fuels the Muslim world's sense of moral outrage.

I don't agree with all of Sageman's arguments, especially about the consequences of a quick drawdown in Iraq, but I think he is raising the questions the country needs to ponder this election year. If Sageman's data are right, we are not facing what President Bush called "the decisive ideological struggle of the 21st century and the calling of our generation," but something that is more limited and manageable -- if we make good decisions.